Could former Telstra CEO Sol Trujillo take a suffering T-Mobile private?

The U.S. telecom industry’s globetrotting and controversial CEO Sol Trujillo may be returning home, not to head up a U.S. operator but to buy one. Trujillo, who formerly headed up baby Bell US West, France Telecom’s(s fte) Orange and Australia’s Telstra, now has his eyes on T-Mobile USA and has approached some big private equity groups for funds to buy it, according to a Bloomberg report.

If we believe Bloomberg’s unnamed sources, Trujillo has pitched Kohlberg Kravis and Roberts(s kkr) and The Blackstone Group(s bx) on raising the enormous amount of private equity to separate T-Mobile USA from its [PARENT?] Deutsche Telekom, but both firms balked at the enormous price tag. T-Mobile USA was most recently valued at $39 billion by AT&T(s t), which unsuccessfully tried to acquire it. According to Bloomberg, Trujillo is also floating the idea of a private equity buyout of Sprint(s s), but at nearly twice T-Mobile’s size would be an even harder sell.

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Trujillo appears to be hitting some roadblocks, but if he eventually finds an investor, it would certainly be an interesting situation for the U.S. wireless industry. Private equity buyouts of large wireless operators certainly aren’t unheard of. In 2007, TPG Capital and Goldman Sachs Capital Partners bought the country’s fifth largest operator Alltel for $27.5 billion and a year later sold it to Verizon(s vz)(s vod) for $28.1 billion.

There are a few differences between Alltel and T-Mobile though – and not just the fact that T-Mobile is three times bigger than Alltel was before its sale. Alltel operated mainly in rural markets and small and mid-sized cities. T-Mobile is in the major metro markets where spectrum is valued at a premium. In addition, TPG and GS bought Alltel to prep it for an eventual sale to a large operator. Such a transaction wouldn’t be so easy with T-Mobile.

The FCC and the U.S. Department of Justice have made it very clear they aren’t letting any of the big 4 carriers merge any time soon. Regulators also would look unkindly at Trujillo trying to dismantle the company and sell off its parts. That means Trujillo and company would have to shop T-Mobile around to companies without current U.S. wireless businesses such as Google(s goog), Apple(s aapl), Dish Network(s dish) or any number of multinational carrier groups. Either that, or Trujillo envisions taking T-Mobile public.

The roving chief executive might have a lot more in common with a scrappy T-Mobile than with Australia’s big wireless incumbent. During is four-year tenure at Telstra, Trujillo oversaw the launch of the carrier’s Next G network, a wide-ranging mobile broadband network that was the first globally to utilize new HSPA+ technology, boosting theoretical bandwidth to 21 Mbps and later 42 Mbps. Coincidentally, T-Mobile holds both those honors in the U.S.